DiggleGratton            package:spatstat            R Documentation

_D_i_g_g_l_e-_G_r_a_t_t_o_n _m_o_d_e_l

_D_e_s_c_r_i_p_t_i_o_n:

     Creates an instance of the Diggle-Gratton pairwise interaction
     point process model, which can then be fitted to point pattern
     data.

_U_s_a_g_e:

       DiggleGratton(delta, rho)

_A_r_g_u_m_e_n_t_s:

   delta: lower threshold delta

     rho: upper threshold rho

_D_e_t_a_i_l_s:

     Diggle and Gratton (1984, pages 208-210) introduced the pairwise
     interaction point process with pair potential h(t) of the form

 h(t) = ((t - delta)/(rho - delta))^kappa, {    } delta <= t <= rho

     with h(t) = 0 for t < delta and  h(t) = 1 for t > rho. Here delta,
     rho and kappa are parameters.

     Note that we use the symbol kappa where Diggle and Gratton (1984)
     and Diggle, Gates and Stibbard (1987) use beta, since in
     'spatstat' we reserve the symbol beta for an intensity parameter.

     The parameters must all be nonnegative, and must satisfy delta <=
     rho.

     The potential is inhibitory, i.e. this model is only appropriate
     for regular point patterns. The strength of inhibition increases
     with kappa. For kappa=0 the model is a hard core process with hard
     core radius delta. For kappa=infinity the model is a hard core
     process with hard core radius rho.

     The irregular parameters  delta, rho must be given in the call to
     'DiggleGratton', while the regular parameter kappa will be
     estimated.

_V_a_l_u_e:

     An object of class '"interact"' describing the interpoint
     interaction structure of a point process.

_A_u_t_h_o_r(_s):

     Adrian Baddeley adrian@maths.uwa.edu.au <URL:
     http://www.maths.uwa.edu.au/~adrian/> and Rolf Turner
     rolf@math.unb.ca <URL: http://www.math.unb.ca/~rolf>

_R_e_f_e_r_e_n_c_e_s:

     Diggle, P.J., Gates, D.J. and Stibbard, A. (1987) A nonparametric
     estimator for pairwise-interaction point processes. _Biometrika_
     *74*, 763 - 770.

     Diggle, P.J. and Gratton, R.J. (1984) Monte Carlo methods of
     inference for implicit statistical models. _Journal of the Royal
     Statistical Society, series B_ *46*, 193 - 212.

_S_e_e _A_l_s_o:

     'ppm', 'ppm.object', 'Pairwise'

_E_x_a_m_p_l_e_s:

        data(cells)
        ppm(cells, ~1, DiggleGratton(0.05, 0.1))

